The Kohn-Sham system of non-interacting electrons

Let us consider an electron subject to some external potential v(r), for example coming from the Coulombic interaction with the nuclei (with charges Z in a.u. and positions r ) 

In this system we have N electrons, which also interact by Coulombic forces between themselves. All these interactions produce the ground-state electronic density distribution po (ideal, i.e. that we obtain from the exact, 100% correlated wave funetion). Now let us consider 

Let us assume for a while that we have found such a wonder potential wo(f). We will worry later about how to find it in reality. Now we assume the problem has been solved. Can we find p Of course, we can. Since the Kohn-Sham electrons do not interact between themselves, we have only to solve the one-electron equation (with the wonder Uf)) 

Kohn-Sham determinant represents an eigenfunction of the fictitious system. Scientists compared the Kohn-Sham otbitals with the canonical Hartree-Fock orbitals with great interest. It turns out that the diffetenees are small. 

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